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Register a new userAn English translation of L. Eulers Calculations on aerostatic balloons made by the late Mr. Leonhard Euler, as they were found on his blackboard, after his death on 7 September 1783
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Sylvio R Bistafa
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This is an English translation of E579 in which the introductory remarks are in French, while Eulers original text is in Latin. By considering the balance of forces acting on a raising balloon on an isothermal atmosphere, namely the weight of the balloon, the buoyant force, and the aerodynamic drag force, Euler provides closed formulas for the calculation of the maximum altitude reached by the balloon, the altitude for which the velocity is maximum, the maximum velocity attained by the balloon, and the total ascending time.
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This is a translation from Latin of E840 De motu cometarum in orbitis parabolicis, solem in foco habentibus, in which Euler addresses six problems related to comets in heliocentric parabolic orbits. Problem 1: Find the true anomaly of a heliocentric comet from the latus rectum of the orbit and the medium Earth to Sun distance. Problem 2: Find the orbit of a heliocentric comet from three given positions. Problem 3: Knowing the orbit of a comet, and the instant in time in which it dwells in the perihelion, define its longitude and latitude at any time. Problem 4: From two locations of a heliocentric comet, find the inclination of the comets orbit in relation to the ecliptic, and the positions of the nodes. Problem 5: From the time before or after the comet had reached the perihelion, and from the comets distance to the perihelion as seen from the Sun, find the same distance in another time before or after it had appeared in the perihelion. Problem 6: Find the orbit of a comet from three given heliocentric longitudes and latitudes. From these problems, several corollaries and scholia are derived.
Boris R. Vainberg was born on March 17, 1938, in Moscow. His father was a Lead Engineer in an aviation design institute. His mother was a homemaker. From early age, Boris was attracted to mathematics and spent much of his time at home and in school working through collections of practice problems for the Moscow Mathematical Olympiad. His first mathematical library consisted of the books he received as one of the prize-winners of these olympiads.
On this, the occasion of the 20th anniversary of the Ising Lectures in Lviv (Ukraine), we give some personal reflections about the famous model that was suggested by Wilhelm Lenz for ferromagnetism in 1920 and solved in one dimension by his PhD student, Ernst Ising, in 1924. That work of Lenz and Ising marked the start of a scientific direction that, over nearly 100 years, delivered extraordinary successes in explaining collective behaviour in a vast variety of systems, both within and beyond the natural sciences. The broadness of the appeal of the Ising model is reflected in the variety of talks presented at the Ising lectures ( http://www.icmp.lviv.ua/ising/ ) over the past two decades but requires that we restrict this report to a small selection of topics. The paper starts with some personal memoirs of Thomas Ising (Ernsts son). We then discuss the history of the model, exact solutions, experimental realisations, and its extension to other fields.
John Adams acquired an unrivalled reputation for his leading part in designing and constructing the Proton Synchrotron (PS) in CERNs early days. In 1968, and after several years heading a fusion laboratory in the UK, he came back to Geneva to pilot the Super Proton Synchrotron (SPS) project to approval and then to direct its construction. By the time of his early death in 1984 he had built the two flagship proton accelerators at CERN and, during the second of his terms as Director-General, he laid the groundwork for the proton-antiproton collider which led to the discovery of the intermediate vector boson. How did someone without any formal academic qualification achieve this? What was the magic behind his leadership? The speaker, who worked many years alongside him, will discuss these questions and speculate on how Sir John Adams might have viewed todays CERN.
This is a translation from Latin of E348 Methodus facilis motus corporum coelestium utcunque perturbatos ad rationem calculi astronomici revocandi, in which Euler develops a method to alleviate the astronomical computations in a typical celestial three-body problem represented by Sun, Earth and Moon. In this work, Eulers approach consists of two parts: geometrical and mechanical. The geometrical part contains most of the analytical developments, in which Euler makes use of Cartesian and spherical trigonometry as well - the latter not always in a clear enough way. With few sketches to show the geometrical constructions envisaged by Euler - represented by several geometrical variables -, it is a hard to follow publication. The Translator, on trying to clear the way to the non-specialized reader, used the best of his abilities to add his own figures to the translation. In the latter part of the work, Euler particularizes his developments to the Moon, ending up with eight coupled differential equations for resolving the perturbed motion of this celestial body, which makes his claim of an easy method as being rather fallacious. Despite showing great analytical skills, Euler did not give indications on how this system of equations could be solved, which renders his efforts practically useless in the determination of the variations of the nodal line and inclination of the Moons orbit.
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